Implementation in MATLAB of the Iso-Geometric Boundary Elements Method for the resolution of 2D anisotropic elastostatic problems

Abstract

In this work, the implementation of the Isogeometric Boundary Element Method (IGABEM) in MATLAB for the resolution of bi-dimensional anisotropic elastostatic problems is presented. This builds on the degree’s final project of this author, which studied the IGABEM for the isotropic case Firstly, some basics about anisotropic elasticity are given, mostly to clarify nomenclature. Secondly, an introduction to the traditional Boundary Element Method (BEM) is offered, explaining the physics behind it and later particularizing the equations for its numerical implementation. The most important details, or those that take relevance when compared to the IGABEM, are commented. Subsequently, the same process is repeated with the IGABEM, adapting all the equations to this method’s features. The implemented MATLAB code is briefly commented, its difficulties and limitations highlighted. Finally, a comparison between the two methods is done. Analysis are carried out in two elastic problems, one orthotropic and one purely anisotropic, and the results are tested. This does not only show the difference in accuracy but also serves to spot better the differences between these two methods and the advantages of one over the other. Finally, some options for further work are discussed. Together with the ideas, an outline of how they would be made and why they would be useful or interesting is made.